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Proc. R. Soc. B (2007) 274, 2077–2086
doi:10.1098/rspb.2007.0515
Published online 26 June 2007
Trophic network models explain instability of Early
Triassic terrestrial communities
Peter D. Roopnarine1,*, Kenneth D. Angielczyk1, Steve C. Wang2
and Rachel Hertog1
1
Department of Invertebrate Zoology and Geology, California Academy of Sciences, 875 Howard Street,
San Francisco, CA 94103, USA
2
Department of Mathematics and Statistics, 500 College Avenue, Swarthmore College, Swarthmore, PA 19081, USA
Studies of the end-Permian mass extinction have emphasized potential abiotic causes and their direct
biotic effects. Less attention has been devoted to secondary extinctions resulting from ecological crises and
the effect of community structure on such extinctions. Here we use a trophic network model that combines
topological and dynamic approaches to simulate disruptions of primary productivity in palaeocommunities. We apply the model to Permian and Triassic communities of the Karoo Basin, South Africa, and
show that while Permian communities bear no evidence of being especially susceptible to extinction, Early
Triassic communities appear to have been inherently less stable. Much of the instability results from the
faster post-extinction diversification of amphibian guilds relative to amniotes. The resulting communities
differed fundamentally in structure from their Permian predecessors. Additionally, our results imply that
changing community structures over time may explain long-term trends like declining rates of Phanerozoic
background extinction
Keywords: mass extinction; end-Permian extinction; Karoo Basin; food webs; extinction cascades
1. INTRODUCTION
Mass extinctions represent times of severe ecological crisis
in the Earth’s past. The history of mass extinctions
documented in the fossil record is one of the geosciences’
crucial contributions to the assessment of human impact
on the Earth today (May 2001). Although numerous
studies have focused on distinguishing background from
mass extinctions, measuring extinction magnitudes, identifying primary abiotic causes, searching for clade-based
selectivity and examining biotic recovery (Sepkoski 1996;
Solé et al. 2002; Benton & Twitchett 2003; Wang 2003;
Lockwood 2004; Jablonski 2005), less attention has been
paid to the role of community structure in the propagation
of or resistance to perturbative mechanisms. Understanding the influence of community structure on responses to
extinction mechanisms is important because many of the
species that went extinct during these episodes probably
did so in response to cascading secondary effects on their
ecological communities ( Vermeij 2004; Angielczyk et al.
2005; Roopnarine 2006). Moreover, even if the physical
nature of mechanisms that cause mass extinctions varied
little during the Phanerozoic, the structures and compositions of affected communities and ecosystems have
changed significantly ( Vermeij 1977; Bambach 1993;
McGhee et al. 2004; Wagner et al. 2006).
The largest mass extinction recorded in the fossil
record is the end-Permian mass extinction (approx.
251 Myr ago). It has been estimated that at least 80% of
all marine invertebrate animal species and up to 74% of
* Author for correspondence ([email protected]).
Electronic supplementary material is available at http://dx.doi.org/10.
1098/rspb.2007.0515 or via http://www.journals.royalsoc.ac.uk.
Received 17 April 2007
Accepted 4 June 2007
terrestrial animal families disappeared at this time (Erwin
et al. 2002; Benton & Twitchett 2003; Benton et al. 2004;
Ward et al. 2005), and the post-extinction Early Triassic
world was characterized by degraded terrestrial and
marine ecosystems (Looy et al. 1999; Pruss & Bottjer
2004). We investigated the potential role of community
structure in this event using a numerical network
simulation model (cascading extinction on graphs, CEG)
to examine the extent to which food-web topology
promotes or inhibits the propagation of disruptions
through a community (Roopnarine 2006). We measure
community resistance as the number of secondary
extinctions resulting from a specific disruption or perturbation, with secondary extinction defined as the extinction
of a species owing to the elimination of dependencies on at
least one other species within the community.
We applied the CEG model to three terrestrial,
tetrapod-dominated palaeocommunities from the Late
Palaeozoic and Early Mesozoic of the Beaufort
Group, Karoo Basin, South Africa: the Middle Permian
Eodicynodon, end-Permian Dicynodon and the Early
Triassic Lystrosaurus biostratigraphic assemblage zones
(Wordian, Changhsingian and Induan–Olenekian stages,
respectively; Rubidge 1995, 2005). The Dicynodon and
Lystrosaurus zones occur immediately before and immediately after the end-Permian mass extinction, respectively.
We focused on bottom-up disruptions of primary productivity for three reasons. First, considerable evidence
indicates widespread declines in primary production
during several major biodiversity crises, including the
end-Permian and Cretaceous–Tertiary extinctions
(Zachos et al. 1989; Knoll et al. 1996; Looy et al. 2001).
Second, the modern biodiversity crises, comprising
primarily the loss of species of high trophic levels owing
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Trophic network models
to habitat destruction or overexploitation, have not yet led
to major top-down propagations of secondary extinctions
( Vermeij 2004), though the effects of top-down trophic
cascades can be demographically significant (Myers et al.
2007). Third, the increasing human exploitation of species
at lower trophic levels, our expanding control of photosynthetic resources (Diamond 2005) and the growing risk
of bottom-up perturbations driven by climate change (Orr
et al. 2005) heighten the need to understand the potential
of cascading-up effects.
(a) Metanetwork properties
The first step in applying the CEG model to the
palaeocommunities is the construction of an ecologically
plausible guild-level representation of trophic relationships within each community, termed a metanetwork.
Each guild consists of species with the same potential prey
and predators, and links between guilds represent sets of
potential trophic interactions (see the electronic supplementary material, table 1). Links were assigned using
simple rules based on fundamental ecological principles
and morphological characteristics of the organisms in the
various communities. In this sense, guilds are estimations
of trophic species, a concept used frequently in the
reconstruction of modern food webs, and represent sets
of species with identical prey and predators (Briand &
Cohen 1984; Williams & Martinez 2000). However, our
guilds reflect palaeobiological uncertainty in the specification of identical sets of predators and prey to different
fossil species.
Published connectances for modern communities
(connectance measured as the ratio of links between
trophic species to the square of trophic species richness)
range from 0.026 to 0.315 (Dunne et al. 2002a,b). The
connectances of our Karoo metanetworks fall within
this range: Eodicynodon, 0.204; Dicynodon, 0.194 and
Lystrosaurus, 0.285. We expect our values to be towards
the high end of the modern range because metanetwork
guilds include more taxa than do trophic species, making
community guild richness lower than trophic species
richness. Our reconstruction of a highly resolved food web
for the modern marine community of San Francisco Bay,
comprising 1312 invertebrate and vertebrate species
assigned to guilds using the same rules that were applied
to the Karoo metanetworks, yields a connectance of 0.192,
showing that our methodology generates reasonable
food webs when applied to modern data (data
available at http://zeus.calacademy.org/SFBaynetwork).
The Lystrosaurus zone metanetwork has an anomalously
greater connectance compared with other zones in the
Beaufort Group (figure 1), primarily owing to the greater
representation of amphibian guilds relative to amniote
guilds. Since Early Triassic amphibians were closer
ecological analogues to extant crocodilians than to most
extant lissamphibians, we reconstructed amphibians in all
zones as feeding at multiple trophic levels both ontogenetically and as adults, and in freshwater and
terrestrial habitats.
(b) Species-level food webs
It is impossible to precisely reconstruct species-level food
webs for palaeocommunities due to the incompleteness of
the fossil record. We therefore used metanetwork data and
link distributions to stochastically generate a large number
Proc. R. Soc. B (2007)
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no. of links in metanetwork
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100
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Figure 1. Connectance or density of interguild links for
eight Permo–Triassic stratigraphical assemblage zone communities from the Karoo Basin. 1, Eodicynodon (Wordian); 2,
Tapinocephalus (Capitanian); 3, Pristerognathus (Capitanian–
Wuchiapingian); 4, Tropidostoma ( Wuchiapingian); 5,
Cistecephalus (Wuchiapingian); 6, Dicynodon (Changhsingian);
7, Lystrosaurus ( Induan–Olenekian) and 8, Cynognathus
(Olenekian–Anisian). All communities follow a linear relationship ( yZ7.85xK75.64, r 2Z0.99), with the exception of
Lystrosaurus (which was excluded from the regression).
Palaeocommunity metanetworks are illustrated for the
Eodicynodon, Dicynodon and Lystrosaurus assemblage zones.
Spheres represent guilds: green, primary producers; blue,
aquatic (freshwater) taxa; purple, insects; red, amphibians
and yellow, amniotes. Insect, amphibian and amniote guilds are
divided among herbivorous, carnivorous and omnivorous
habits. Links between guilds represent sets of trophic
interactions.
of possible species-level networks, rather than attempting
a single static reconstruction. We thus account for two
important sources of uncertainty in our knowledge of
actual food webs, as well as their temporal and spatial
variability. First, the exact number of trophic interactions
that any fossil species would have possessed or the
particular species with which it interacted cannot be
known, even though we have a good idea of its interactions
at the guild level. Second, food-web topologies of specific
communities are probably flexible in both time and space
because community structures are dependent on environmental and biotic contexts ( Thompson 1999b,a).
We derived species-level food webs, or palaeotrophic
networks, from the metanetworks using stochastic draws
from guild trophic-link distributions. The trophic-link
distributions are based on measures of the number of
prey per consumer species in Recent communities. Those
measures generally define regular decay distributions, most
often attributed to exponential or power-law functions.
The mixed distributions used in this paper took the form
P(r)Zexp(Kr/3), where 3Zexp((gK1)log M/g), M is the
total number of potential prey species or units of
productivity available and g is the power-law exponent
that determines the extent to which a species can be a
generalist (see the electronic supplementary material,
figure 1). Link distributions converge to an exponential
distribution of the form described for a variety of modern
food webs (Camacho et al. 2002) as g approaches 1. The
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factor 3 reflects the point at which a power-law distribution
of exponent g would yield the minimum number of prey for
any consumer species. However, the true algorithmic
minimum for the mixed distributions was 1, and the
distributions were always truncated to yield no more than
M interactions. This process yielded distributions of
trophic habits for species within guilds ranging from
specialist to generalist feeders, reflecting distributions
estimated empirically from modern communities
(Camacho et al. 2002; Montoya et al. 2006). All the
networks we generated using this procedure possessed link
densities within the range observed for modern, specieslevel and aggregated food webs (Pimm et al. 1991; Havens
1992; Martinez 1992; see the electronic supplementary
material, table 2).
(c) Determining secondary extinction
We employed two approaches to determine whether a
species’ population became secondarily extinct following a
perturbation. First, we derived analytical solutions using
the network topological approach, in which a population
becomes extinct if all the nodes (species) or units of
productivity to which it is linked are lost (Dunne et al.
2002b). The topological approach is amenable to the
analysis of very diverse and complicated networks, and its
application to modern communities has led to a general
conclusion that increased connectance among trophic
species raises resistance to secondary extinction (Dunne
et al. 2002b; Eklöf & Ebenman 2006). Second, since
populations that do not become topologically extinct are
nonetheless likely to be affected by perturbations to the
community, we also employed a dynamic approach that
incorporated the demographic properties and interactions
of populations. In theory, combined topological and
dynamic extinctions could be written in terms of classical
interspecific dynamics, but the sheer number of
interactions quickly renders this approach intractable for
communities of even modest diversity (hundreds of
species) and connectance (Montoya et al. 2006; Shipley
et al. 2006). We therefore used systems of difference
equations and numerical simulations to combine the
two approaches.
Individual species populations in the CEG model
possess several important network parameters, including
an in-degree measuring the number of prey resources and
an out-degree measuring the number of predators.
Interspecific trophic-link properties include the strengths
of biotic interactions and the demographic state of each
population. We parameterize consumer in-links using
interaction strengths, with individual interaction strengths
being inversely proportional to the number of prey links or
interactions of the population (Roopnarine 2006). If the
state of a population is considered to be a balance between
incoming energy and energy lost to predation, then
parameterization of the trophic network yields a standardized population size that can be determined for each
species. Secondary extinction occurs in a simulation if the
population size falls below a threshold level, the minimum
viable population size (MVP). MVP sizes were set in the
simulations to specify the size at which a population (i)
became functionally extinct within the community, (ii)
was doomed to extinction owing to environmental or
demographic stochasticity (e.g. Allee effects), or (iii) had
declined to zero population size. Conceptually, MVP in
Proc. R. Soc. B (2007)
topological secondary extinction
Trophic network models
P. D. Roopnarine et al.
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Figure 2. Expected topological secondary extinction for
Eodicynodon (black curve), Dicynodon (blue curve) and
Lystrosaurus (red curve) assemblage zone communities.
Perturbation magnitude (x -axis) is the proportion of primary
production removed from the systems, and topological
secondary extinction ( y-axis) is the proportion of consumer
species expected to go extinct as a result. Secondary
extinction is summed over all guilds in the community.
the CEG model is a function of carrying capacity and is
always given as a fraction of standardized carrying capacity
at zero perturbation (Roopnarine 2006). MVP size can
therefore be set to 0, indicating that the population must
decline to 0 individuals for extinction to occur, or set to 1,
indicating that the population will become extinct
immediately under any conditions, or it can be set to a
value between 0 and 1, indicating the fraction of the preperturbation population size at which extinction will
occur. Different MVP sizes among guilds reflect the
greater susceptibility of some guilds of consumers to
extinction. For example, larger animals, particularly
carnivores, tend to have greater sensitivities to perturbations, and hence greater MVP size, owing to smaller
equilibrium population sizes, as well as factors such as
greater range requirements (Brown 1995). Those larger
consumers, on the other hand, also tend to have broader
dietary repertoires as a function of larger size, for example
owing to larger and more efficient digestive systems, or the
ability to handle a wider array of prey. Large consumers in
our model would therefore have higher MVP sizes, but
greater numbers of incoming links. Varying MVP sizes did
not, however, alter our results significantly.
2. RESULTS
(a) Analytic estimations
We applied bottom-up disruptions of productivity to
Karoo species-level networks by reducing the level of
productivity in one or more primary producer guilds. We
then used numerical simulations to assess the total effects
of the disruptions to the palaeocommunities, including
feedback and indirect interactions. We also analytically
estimated the expected topological effects of the initial
perturbation to the systems. Given the stochasticity in
topological specification of the species-level networks, the
probability of topological secondary extinction of any
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consumer population, after the removal or loss of
resources, declines as the consumer’s in-degree or number
of prey species increases (see §4 and the electronic
supplementary material, figure 2). A comparison of
expected topological secondary extinction for typical
Eodicynodon, Dicynodon and Lystrosaurus zone communities suggests that Lystrosaurus zone communities should
have been marginally more resistant to secondary extinction than the earlier communities (figure 2). This result is
unsurprising given the greater guild-level connectance of
the Lystrosaurus metanetwork and expectations of the
topological perspective (Dunne et al. 2002b).
Topological secondary extinctions are expected to
trigger cascading secondary effects among survivors.
These additional impacts stem from the demographic
effects of the perturbation on surviving populations.
Although the complexity of the interspecific demographic
interactions prohibits a thorough analytical treatment, we
investigated the impact of the initial perturbation by
estimating the number of interactions lost by surviving
populations, as well as subsequent changes to the
strengths of surviving interactions. Populations survive
the perturbation either because they are immune to
topological secondary extinction (i.e. their resources
exceed the magnitude of the perturbation), or because
despite being susceptible, they were statistically lucky.
By estimating the number of interactions that are expected
to persist in each metanetwork after a perturbation, we
found that very few links were lost by populations that
survived initial disruptive pulses (see §4). Moreover, the
fraction of links lost did not increase linearly or rapidly as
perturbation magnitude increased (see the electronic
supplementary material, figure 3), although the strengths
of remaining interactions did compensate for lost links.
Since we model individual interaction strength as the
inverse of the number of interactions, as other resources
experience secondary extinction, we expect individual
species to compensate by increasing interaction strengths
with remaining resources. However, the secondary loss of
species was more rapid than the loss of interactions by
surviving species, and summed interaction strength at the
guild level declined in a stepwise fashion as the magnitude
of perturbation was increased (see the electronic supplementary material, figure 4). Therefore, even though
survivors do respond to the loss of resources from lower
trophic levels by increasing the strengths of their
remaining interactions, the total interaction strength
exerted by one guild on another of lower trophic level
decreased as bottom-up perturbation increased and more
consumer species experienced secondary extinction.
(b) Numerical simulations
Continued analytical prediction of community behaviour
is difficult beyond the initial bottom-up propagation of the
perturbation. Surviving consumers compensate, thereby
initiating top-down effects, creating the potential for
continued and complex secondary interactions and
additional extinctions. Furthermore, topological metanetwork features in which members of one or two guilds
potentially prey on each other, such as loops and
bidirectional links, are difficult to address analytically,
yet exist in our metanetworks. We addressed these
problems with numerical simulations of bottom-up
perturbations, incorporating the full set of metanetwork
Proc. R. Soc. B (2007)
features, and combined topological and demographic
(dynamic) secondary extinctions. We refer to this as
combined secondary extinction.
The Karoo communities responded topologically to the
initial perturbation, but subsequent dynamic top-down
cascades were initiated by surviving consumers, in turn
reinforcing bottom-up effects and ultimately generating
positive feedback loops. Under these conditions, levels of
secondary extinction were greater than those resulting
from topological effects alone (figure 3), supporting the
position that topological analysis predicts lower levels of
secondary extinction than dynamic analysis (Eklöf &
Ebenman 2006) and justifying our combined approach.
Simulations of combined secondary extinction in the
Permian Eodicynodon and Dicynodon zone communities
using broad trophic-link distributions were quite resistant
over a wide range of perturbation magnitudes, exhibiting
some secondary extinction but eventually settling to new
stable states (figure 3a, f ). However, there are perturbation thresholds beyond which secondary extinction rose
both rapidly and catastrophically. This result is explained
by the topologically triggered loss of highly linked
consumers that are immune at lower perturbation levels
(Dunne et al. 2002b; Roopnarine 2006), and the transition
from a predominance of secondary extinctions caused by
external perturbation-driven dynamics to extinctions
resulting from internally driven demographic interactions.
In contrast, Triassic Lystrosaurus zone communities had
highly variable and unpredictable responses, often exhibiting high levels of secondary extinction even at low levels of
perturbation (figure 3k).
3. DISCUSSION
(a) Community basis of Early Triassic instability
Do these results imply that Lystrosaurus zone communities
were inherently less stable than preceding communities?
Such a conclusion would be congruent with observations
that the Early Triassic was a time of environmental and
ecological instability (deWit et al. 2002; Benton et al.
2004; Pruss & Bottjer 2004; Payne & Kump 2007). If
correct, this implies that community structure itself
contributed to the instabilities observed in the geological
record. The major differences between the Lystrosaurus
zone communities and those of the Eodicynodon and
Dicynodon zones were their systematic and ecological
compositions. Recall that Lystrosaurus zone communities
were amphibian-dominated and possessed more connections per guild compared with the other amniotedominated communities. The result was a greater
connectance of the Lystrosaurus metanetwork (figure 1),
and correspondingly greater dynamic amplification of
perturbations and feedback among guilds, leading to
higher levels of combined secondary extinction.
However, the instability of the Early Triassic community can be moderated by manipulating a single set of
parameters in the model, namely g, the power-law
exponents of the guild link distributions that control
network connectance at the species level. We employed
values of 3 for every guild in the initial simulations
(figure 3a, f,k), but repeating the simulations over a range
of g values between 1 and 3 for the three zones
demonstrated a general trend of increasing resistance
to secondary extinction as g increased (figure 3).
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0.6
(a)
(f)
(k)
(b)
( g)
(l)
(c)
(h)
(m)
(d )
(i)
(n)
(e)
( j)
(o)
P. D. Roopnarine et al.
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secondary extinction
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Figure 3. Levels of secondary extinction resulting from numerical simulations of perturbations to 100 stochastically generated
food webs for each palaeocommunity. (a–e) Eodicynodon, ( f–j ) Dicynodon and (k–o) Lystrosaurus zone networks. Simulations
were repeated for networks generated with trophic-link distribution power-law exponents of 1 (e, j,o), 1.5 (d,i,n), 2 (c,h,m), 2.5
(b,g,l ) and 3 (a, f,k). Secondary extinction ( y-axis) measures the total (topologicalCdynamic) proportion of species that became
extinct in response to the perturbations. Note that the distribution of results for Lystrosaurus zone networks is much broader
compared with the other two zones, highlighting the lower predictability of responses of those networks to perturbation.
This remains true even as increasing g values reduce the modes of the distributions of secondary extinction at specific
perturbation magnitudes.
Ecologically, increasing g corresponds to increasing
dietary breadth within guilds, leading to greater proportions of generalist species at higher values of g. Highly
connected generalist species have lower probabilities of
topological secondary extinction and generate less intense
top-down compensatory feedback owing to lower per
capita interaction strengths (although they do contribute
more significantly to the phenomenon of catastrophic
crashes). Therefore, in general, holding the metanetwork
topology (relationships among guilds) constant while
increasing the proportion of generalist species within
guilds produces communities that are more resistant to
secondary extinction. This raises the possibility of longterm community-level selection based on the emergent
property of species’ dietary breadths. Selection for
communities that are more resistant to secondary
extinction could explain, at least partially, apparent trends
such as declining rates of background extinction over the
Phanerozoic (Raup & Sepkoski 1982). Selection at this
level would also favour communities with guilds
Proc. R. Soc. B (2007)
increasingly dominated by generalists (and hence greater
values of g). Increasing the proportion of generalists,
however, yields diminishing returns as values of g exceed 2
(figure 4), and any higher-level selection for communities
composed increasingly of extreme generalists would
probably be offset or overwhelmed by the advantages of
population-level selection for dietary specialization and
coevolved biotic interactions ( Vermeij 2004).
We are also led to question the variability of actual
Lystrosaurus zone communities. Unlike Eodicynodon and
Dicynodon zone communities, whose responses to perturbation are uniform within the range of our stochastic
reconstructions, Lystrosaurus zone communities have
highly variable responses. This could mean that some
real Lystrosaurus zone communities were very unstable and
experienced frequent compositional turnover in response
to an unstable environment. On the other hand,
Lystrosaurus zone communities could have been as stable
as their predecessors if only a small fraction of the range of
stochastic reconstructions, in the region of low secondary
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2082 P. D. Roopnarine et al.
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boundary has made the lower portions of the Lystrosaurus
assemblage zone one of the best-known portions of the
entire Karoo sequence (Botha & Smith 2006). The
number of fossils collected from the Lystrosaurus zone is
also relatively high when compared with other zones
(M. Nicolas 2007, personal communication), and the full
spectrum of body sizes known from the other communities
is present. Finally, although continued collecting has
uncovered new species in the Lystrosaurus zone (Modesto
et al. 2003), these species generally are members of guilds
that were already represented in the assemblage.
topological secondary extinction
1.0
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g = 2.5
g =3
0
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perturbation magnitude
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Figure 4. Expected topological secondary extinction for
Lystrosaurus zone communities, applying trophic-link distributions with values of g ranging from 1 to 3. The level of
secondary extinction decreases as g increases, but by ever
diminishing amounts.
extinctions, was realized in actual communities. If true,
this would imply that animals in Lystrosaurus zone
communities were significantly more constrained in their
trophic habits than were their ecological predecessors
because deviations from a limited set of interactions could
precipitate the collapse of their communities.
There is a paradox here associated with the hierarchical
organization of communities. More highly connected, or
generalized, species are more resistant to secondary
extinction because they use a greater diversity of resources.
More highly connected communities, or metanetworks,
however, seem to generate higher levels of secondary
extinction and global instability owing to the greater
linkage among different sections of the communities. The
Lystrosaurus zone metanetwork amplified perturbation
effects to a greater degree, in comparison with the
Eodicynodon and Dicynodon zones, owing to the greater
connectance among its guilds, and regardless of specieslevel connectances. Perhaps such unstable community
topologies cannot normally exist under disruptive conditions, but the unusual ecological and taxonomic
conditions present in the aftermath of a mass extinction
may provide a window of opportunity, albeit a brief one.
(b) Taphonomic considerations
These observations also raise the question of whether the
unusual structure of the Lystrosaurus zone community was
a direct result of the effects of the end-Permian mass
extinction, or if our reconstructions have been influenced
by a taphonomic bias that resulted in a skewed picture of a
normally structured community. Although the preservational environment of the Lystrosaurus zone appears to
have differed from that of the Permian zones (Smith &
Botha 2005), we doubt the significance of taphonomic
biases for several reasons. First, collector effort has been
spread uniformly across the whole of the Beaufort Group
in the Karoo Basin, implying that the unusual faunal
composition of the Lystrosaurus zone is not simply the
result of inadequate exploration of exposed strata of this
age (M. Nicolas 2007, personal communication). Second,
recent detailed collecting near the Permo–Triassic
Proc. R. Soc. B (2007)
(c) Conclusions
In summary, ecological communities are complex adaptive systems (Gell-Mann 1994) whose particular topologies are expected to vary through time and space, even if
rules of community assembly remain static. This variability means that we cannot rely on the prediction of
specific outcomes from specific perturbations. Instead, we
must predict distributions of potential outcomes, as
exhibited most dramatically by the Lystrosaurus zone
communities. This distinction becomes evermore important as community complexity increases. Whatever the
specific topological details of the three Karoo Basin
community types might have been, the response of postmass extinction Lystrosaurus zone communities to disruptions of productivity would have been inherently less
predictable and potentially more disastrous. Finally, the
application of dynamic community models to palaeoecological data has the potential to yield insight into both the
resistance to and recovery from episodes of mass
extinction, as well as apparent Phanerozoic trends such
as the declining rate of background extinction.
APPENDIX. MATERIAL AND METHODS
(a) Metanetwork reconstruction
The first step in constructing metanetworks for the communities consisted of compiling a list of vertebrate genera
reported from each of the three assemblage zones, based on
lists from literature reports (Rubidge 1995; Schoch & Milner
2000; Angielczyk & Kurkin 2003; Modesto et al. 2003;
Damiani & Rubdige 2004; Sidor & Smith 2004), and
K. Angiekzyk 2002–2006, personal observations. Although
the Permian–Triassic transition in the Karoo has received
much attention (MacLeod et al. 2000; Ward et al. 2000;
Smith & Ward 2001; Retallack et al. 2003; Steiner et al. 2003;
De Kock & Kirschvink 2004; Smith & Botha 2005; Ward
et al. 2005), precise correlations and detailed faunal lists do
not exist for all localities assigned to a particular assemblage
zone (although see Kitching 1977). Therefore, all taxa
reported from an assemblage zone were treated as a single
palaeoecological community. This is a simplification because
not all taxa reported from a given zone have stratigraphical or
spatial ranges spanning the entire zone (e.g. Rubidge 1995;
Smith & Ward 2001; Ward et al. 2005; Botha & Smith 2006).
Additionally, it has recently been suggested that it may be
possible to further subdivide the Lystrosaurus assemblage
zone into a series of temporally successive subcommunities
(Botha & Smith 2006). However, the stratigraphical ranges of
a number of Lystrosaurus zone taxa are insufficiently well
constrained to allow their definite assignment to one or more
of these subcommunities at this time.
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Trophic network models
We next assigned vertebrate genera from each assemblage
to series of guilds. These assignments were sometimes
simplistic (e.g. all aquatic non-tetrapod vertebrates were
assigned to a single fish guild), but they usually were based on
body size, inferred diet and phylogeny. Terrestrial tetrapods
were divided into herbivore and faunivore guilds on the basis
of cranial and dental morphology, with additional consideration of the dietary hypotheses of previous workers (see the
electronic supplementary material, table 1). The herbivore
and faunivore guilds were further subdivided into five body
size classes, using skull length as a proxy: very small
(skull length 0–100 mm), small (101–200 mm), medium
(201–300 mm), large (301–400 mm) and very large (401 mm
and above). This process yielded a total of 10 guilds.
Amphibian taxa were divided into the same body size classes,
but were placed in separate amphibian guilds, reflecting
dietary differences between them and terrestrial tetrapods.
The amphibian guilds added another five potential guilds to
each community. Not all amphibian or amniote guilds were
present in each community.
All tetrapod herbivores fed on one primary producer guild
(terrestrial productivity available to tetrapods and insects)
that included a potentially large number of producer species
and food sources. Treating these producers as a single guild
reflects the fact that there are no arboreal or flying tetrapods
in any of the communities, which when combined with the
generally short stature of Permian and Triassic tetrapods
implies that a significant amount of primary productivity was
simply out of reach of the terrestrial vertebrates. Terrestrial
faunivores were assigned links to terrestrial herbivore and
faunivore guilds up to two size classes larger and two size
classes smaller than themselves. For example, medium-sized
faunivores could feed on very small, small, large and very
large terrestrial herbivores and faunivores. This accounts for
the fact that any particular faunivore species probably
consumed adult individuals of species smaller than itself,
and juveniles of species larger than itself. The two smallest
terrestrial faunivore guilds also were assigned links to insects
and myriapods. Amphibian guilds were given more catholic
diets, although all were assumed to be faunivorous. An
amphibian guild could feed on other amphibian guilds up to
two size classes larger or smaller than itself, terrestrial
herbivores and faunivores up to two size classes larger or
smaller than itself, fishes and aquatic insects. Given these
diets, amphibians link the dry and freshwater components of
the communities. The single fish guild in each community
had predatory links to one source of primary productivity
(aquatic macrophytes), all amphibian and insect guilds
(assuming that some members of these guilds had aquatic
larval or adult stages) and all aquatic non-insect invertebrates.
It is doubtful that any herbivore guilds exhibited significant
omnivory because all probably fed only at the primary
producer level and do not show obvious specializations
for faunivory.
The Middle Permian to Middle Triassic insect fossil
record of the Karoo Basin is patchier than the vertebrate fossil
record, with no insect fossils reported from most of the
assemblage zones (Rubidge 1995). However, a diverse insect
fauna has been recovered from a handful of Dicynodon
assemblage zone-age localities in KwaZulu–Natal (Riek
1973, 1974, 1976; Anderson & Anderson 1985, 1997; van
Dijk 1997; van Dijk & Geertsema 1999; Geertsema et al.
2002; Ponomarenko & Mostovski 2005). Because insect
faunas are not known from the Eodicynodon or Lystrosaurus
Proc. R. Soc. B (2007)
P. D. Roopnarine et al.
2083
assemblage zones, the Dicynodon zone insect fauna was used
for all reconstructed communities. This approach is conservative because including the same insect fauna in each
community increases the similarity of the ecological
structures of the communities, as well as their responses to
perturbation. Excluding the insect fauna completely, or
including it only in the Dicynodon assemblage zone, would
exaggerate differences between the assemblages. The insect
fauna consisted of three guilds: insect herbivores, insect
faunivores and insect omnivores (including detritivores).
Because nearly all the relevant fossils consisted of isolated
wings, it was difficult to assign specific diets for each genus.
This problem was addressed by noting to which higher taxon
(usually at the ordinal level) a particular genus was assigned,
reconstructing the basal feeding strategy for that higher taxon
using published information (Rasnitsyn & Quicke 2002;
Grimaldi & Engel 2005). This approach provided the best
combination of rigor and consistency in the dietary
reconstructions. Herbivorous insects were allowed to feed
on all four producer guilds. Faunivorous insects were allowed
to feed on all insect guilds (including faunivorous insect
species), as well as on myriapods (when present). Omnivorous
insects were linked to all four sources of primary
productivity, all three insect guilds (including themselves)
and myriapods.
Few non-insect invertebrates are known from the Middle
Permian to Middle Triassic assemblages of the Karoo Basin
(van Dijk 1981; Anderson & Anderson 1985; Rubidge
1995). Our metanetworks included a maximum of three
non-insect invertebrate guilds: molluscs, conchostracans and
myriapods. Molluscs and conchostracans fed only upon
aquatic microphytes. The myriapods fed on two sources of
primary productivity (terrestrial productivity available to
tetrapods and insects and terrestrial productivity available
only to insects).
Productivity is difficult to measure in the geological record
and is often expressed as the temporal and/or spatial variation
of proxy measurements (e.g. d13C). However, the network
nature of the CEG model specifies trophic links of primary
consumers to producers. The Karoo Basin has produced wellstudied Permian and Triassic fossil floras (e.g. Anderson &
Anderson 1985), but correlations between the plant
localities and tetrapod-bearing strata, especially with regard
to the Permo –Triassic boundary, are not exact (Gastaldo
et al. 2005). Therefore, detailed reconstructions of the Karoo
producer communities were not attempted. Nevertheless,
any palaeocommunity that is preserved in the fossil record
must have possessed sufficient levels of primary production to
support the consumers, and we can parameterize the model
on the basis of initial consumer demand (when perturbation
is absent). The number of available units of primary
production was thus fixed for all metanetworks as 10 times
the maximum species richness of primary consumer guilds,
reflecting the thermodynamic scaling of energy transfer
among trophic levels (repeating simulations at levels 20, 30
and 40 times, the maximum species richness of primary
consumer guilds did not alter results qualitatively). Units of
primary production were subdivided into primary producer
guilds according to the proportions of primary consumers of
particular trophic habits (e.g. aquatic microphytes and
suspension/filter feeders versus macrophytes and fishes). We
used four producer guilds: terrestrial productivity available
to tetrapods and insects, terrestrial productivity available only
to insects, aquatic macrophytes and aquatic microphytes.
Downloaded from http://rspb.royalsocietypublishing.org/ on June 17, 2017
2084 P. D. Roopnarine et al.
Trophic network models
All simulations were run with twice the observed generic
consumer diversity present in each guild, implying that each
genus comprised two species. We used this assumption to
account for taxonomic uncertainty and incompleteness in the
fossil record.
(b) Probability of extinction, link loss and interaction
strength
The probability of topological secondary extinction, where a
consumer loses all of its prey resources, is
K1
u
M
pðer juÞ Z
;
ð4:1Þ
r
r
expected number of interactions lost by the guild,
su Z
nr ð1KpðeÞÞ
:
EðLJ juÞ
(c) Demographic interactions
If the state of a population is considered to be a balance
between incoming energy and energy lost to predation, then
parameterization of the trophic network yields a standardized
population size that can be determined for each species as
kj;u Z
jMj j
X
km
mZ1
where r is the consumer’s in-degree or number of prey
species; M is the total number of potential prey or units of
productivity and u is the magnitude of the perturbation (see
the electronic supplementary material, figure 2). The total
expected level of extinction within a consumer guild J
is therefore
EðjJ Þ Z
M
X
pðer Þnr ;
ð4:2Þ
rZ1
where j is the level of secondary extinction; p(er) is the
probability of extinction of a consumer with r in-links and nr is
the expected number of species in J with r in-links and is
calculated as a fraction of the total diversity of J (denoted jJj),
equivalent to the area under the link distribution curve
corresponding to link degree r. Thus,
"Ð
#
r
rK1 PðrÞ
jJj:
nr Z Ð M
0 PðrÞ
The probability that a species that survives a perturbation
will nonetheless lose q interactions out of r is
K1
r
M
pðqÞ Z
:
ð4:3Þ
q
q
The expected number of interactions in guild J that therefore
survive a perturbation of u is
EðLJ juÞ Z L0 K
M
X
½pðqr Þnr C
uC1
u
X
½ðnr K jr Þpðqr Þ;
ð4:4Þ
rZ1
where LJ is the number of surviving interactions; L0 is
the original number of interactions before perturbation; the
second term on the right hand side of the equation is the
number of interactions lost by immune members of J (where
rOu); the third term on the right hand side of the equation is
the number lost by susceptible but surviving members of J
(where r%u); and p(q) is the probability of losing q
interactions out of r (see the electronic supplementary
material, figure 3). p(q) is maximized when rZ1 (yielding
p(q)Zr/M ). The original number of interactions in J prior to
perturbation is
L0 Z
M
X
rnr :
ð4:5Þ
rZ1
The strength of a single interaction of a species with r prey,
in the absence of perturbation, is
1
s0 Z :
r
ð4:6Þ
However, when the community is perturbed and secondary
extinction occurs, the interaction strength is a function of the
probability of the species surviving the perturbation and the
Proc. R. Soc. B (2007)
ð4:7Þ
jNj
X
kn
K
;
rj
r
nZ1 n
ð4:8Þ
where rj is the number of interactions of consumer species’
population j; jMjj is the number of prey species of j; jNj is the
number of species that prey on j; r n is the number of predatory
interactions of j’s predators and k i,u are species population
sizes in guilds J, M and N after a perturbation of magnitude u
(subscripts simplified on right-hand side of formula).
We thank G. J. Vermeij, C. Tang, D. Goodwin and E. Conel
for their many helpful comments and discussions.
M. Kowaleski and an anonymous reviewer provided many
helpful comments and suggestions. M. Olson compiled data
on fishes for the San Francisco Bay food web. R. Van Syoc
kindly assisted with the compilation of invertebrate data from
the Invertebrate Zoology collection at the California
Academy of Sciences. This project was supported by grants
from NSF (EAR-0313560 to P.D.R and ARC-0530825 to
P.D.R. and S.C.W.), the Swarthmore College Research Fund
and the Woodrow Wilson National Fellowship Foundation
(to S.C.W.), and a Royal Society USA/Canada Research
Fellowship (to K.D.A.).
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